Four voters including Andy Erlam, who stood as a council candidate on an anti-corruption ticket, petitioned to get the election result declared void following widespread allegations of fraud and intimidation.

But lawyers for Rahman applied for the high court petition to be dismissed as an abuse of process, saying sufficient particulars of the allegations were not given.

On Tuesday, Mr Justice Supperstone and Mr Justice Spencer said they had reached the firm conclusion, for reasons they would specify later, that the petition was "not a nullity in whole or in part". The ruling is a blow for the mayor, who had hoped to kill off the petition. His team argued that it is a waste of council resources to fight a claim, which they said is being secretly backed by Labour and the Tories.

In the council election, Rahman's Tower Hamlets First party finished a close second to Labour, despite a central government inquiry launched by Eric Pickles.

The inquiry investigated claims that public money had been spent disproportionately on his supporters' pet projects and that council properties were sold to his allies at knockdown prices. Rahman dismisses both claims.

The petition accuses Rahman of being connected to alleged electoral fraud, including the casting of postal votes in the names of people not entitled to be on the electoral register.

It also alleges that votes were illegally cast on behalf of other electors and that activists were paid to lobby people in and around polling stations and that false allegations of racism were made against John Biggs, the losing Labour mayoral candidate.

The courts may now investigate Rahman's election win, with the possibility of the result being overturned.

The high court ruled that the petitioners must produce detailed evidence by 18 August and dismissed their claim for the case to be heard outside Tower Hamlets. It appears likely that the hearing will be held in the local town hall.

In a statement, Rahman said there was no evidence that the recent election results were due to fraud and intimidation.

"It is clear that these complaints are being generated by disgruntled candidates who lost and the court has recognised this by not granting them a protected costs order," he said. "I am completely confident that at the end of this process such claims will be exposed for the smears that they are."

• This article was amended on 29 July 2014. It originally stated that Rahman's Tower Hamlets First party swept to power in the council elections. The party finished second to Labour. This has been corrected.